Method for compensating a magnetic locator, locator and computer program

ABSTRACT

The invention relates to a method for compensating a magnetic locator in the presence of a magnetic-field-disturbing material, comprising: an emitter (10) comprising at least one coil emitting an emission magnetic field; a receiver (20) comprising at least one receiving coil and a device providing a plurality of measurements Ipi of a receiving magnetic field induced by the emission field in each receiving coil; and a processing unit (25) comprising a field model allowing the calculation of a position (P) and/or an orientation (Q) of the receiver by means of calculation of a prediction Hi of the measurements according to a criterion (C) calculated according to an error Ei which is itself calculated in relation to the measurements Ipi. The invention is characterised in that the error Ei is calculated by successive iterations from initial values prescribed by the prediction Hi as being the difference between the measurements Ipi and a disturbed model Hpi, according to the equation Ei=Ipi−Hpi, the disturbed model Hpi satisfying Hpi=Hi+Pi (αi=−arctan(βωi), (I) the parameter β being identical for all of the measurements Ipi, the calculation being carried out in such a way as to minimise the criterion C.

The invention relates to a method for compensating a magnetic locator inthe presence of at least one disruptive material.

A magnetic locator generally comprises a transmitting device, theso-called transmitter, having one or more transmitter coils rigidlyconnected to one another, and a receiving device, the so-calledreceiver, having one or more receiver coils rigidly connected to oneanother. The joint analysis of the magnetic fields transmitted by thetransmitter coils and of the magnetic fields measured by the receivercoils makes it possible to determine by a processing unit the positionand/or orientation of the receiving device with respect to thetransmitting device. This processing unit comprises a field model makingit possible to compute the position and/or orientation of the receiverby computing a prediction of the measurements as a function of acriteria of minimization of an error computed with respect to themeasurements.

The problem of the invention is a material can exist that disrupts themagnetic field between the transmitter and the receiver. In particular,certain electrically conductive materials can give rise to eddy currentswhen these materials are placed in a magnetic field. The eddy currentsthat then circulate in this conductive material in turn generate adisruptive magnetic field.

Thus, the presence of a disruptive material causes errors in thecomputation of the prediction by the processing unit.

The invention aims to solve this problem by proposing a method and adevice for compensating a magnetic locator in the presence of at leastone disruptive material, which make it possible to compute the correctposition and/or orientation of the receiver corresponding as much aspossible to its actual position and/or to its actual orientation,despite the disruptive magnetic field induced by the material.

For this purpose, a first subject of the invention is a method forcompensating a magnetic locator in the presence of at least onemagnetic-field-disrupting material, said magnetic locator comprising:

-   -   at least one transmitter comprising at least one transmitter        coil and at least one generator of at least one transmission        signal, connected to the at least one transmitter coil, so that        the at least one transmitter coil transmits at least one        transmitting magnetic field at at least one determined frequency        ω_(i) in response to the transmission signal that is sent to it        by the generator,    -   at least one receiver comprising at least one receiver coil and        a measuring device, which is connected to the at least one        receiver coil and which supplies at least one measurement Ip_(i)        of a receiving magnetic field respectively induced by the        transmitting magnetic field in each receiver coil, in such a way        as to supply several measurements Ip_(i) for i ranging from 1 to        N,    -   a processing unit comprising a field model making it possible to        compute a position and/or an orientation of the receiver by        computing a prediction H_(i) of the measurements as a function        of a criterion computed as a function of an error E_(i), itself        computed with respect to the measurements Ip_(i),

characterized in that

the error E_(i) is computed by successive iterations from initialprescribed values of the prediction H_(i) as being the differencebetween the measurements Ip_(i) and a disrupted model Hp_(i) of themeasurements, according to the equation

E _(i) =Ip _(i) −Hp _(i),

the disrupted model Hp_(i) of the measurements verifying the followingequations

${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}}$α_(i) = −arctan (β ⋅ ω_(i)),

where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material, ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material, β being a parameter of themagnetic-field-disrupting material,

the parameter β being identical for all the measurements Ip_(i),

the computation being carried out in such a way as to minimize thecriterion.

According to an embodiment of the invention, the field model used tocompute a position and/or an orientation of the receiver by computingthe prediction H_(i) of the measurements as a function of the criterionuses a Levenberg-Marquardt minimization algorithm.

A number of first embodiments are described below. For each embodiment,the following steps described below are carried out in each iteration.

According to a first embodiment of the invention, at each iteration,

-   -   the prediction H_(i) is initialized at the initial prescribed        values,    -   then are computed Δ_(i), the parameter β so as to minimize the        vector A·β−B over its coordinates and the disrupted model Hp_(i)        as a function of H_(i) and Ip_(i) according to the equations

Δ_(i)=[

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i))]/[

(H _(i))²+

(H _(i))²]

Hp _(i) =H _(i)·(1+Δ_(i)·(j+βω _(i))),

where A is a vector, the first and second coordinates of which arerespectively formed by: A_(2i)=Δ_(i)·

(H_(i))·ω_(i) et A_(2i+1)=Δ_(i)·

(H_(i))·ω_(i),

B is a vector, the first and second coordinates of which arerespectively formed by:

B _(2i)=

(Ip _(i))−

(H _(i))+Δ_(i)·

(H _(i)) and B _(2i+1)=

(Ip _(i))−

(H _(i))−Δ_(i)·

(H _(i)),

for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i),

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the invention

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the prediction H_(i) corresponding to the criterion C is        computed by the field model,

this computed prediction H_(i) being used for the following iterationuntil the criterion C becomes less than a prescribed non-zero positivebound η.

Following another first embodiment of the invention, at each iteration

-   -   the prediction H_(i) is initialized at the prescribed initial        values,    -   then are computed Δ_(i), the parameter β and the disrupted model        Hp_(i) as a function of H_(i) and Ip_(i) according to the        equations

$\Delta_{i} = {\lbrack {{{( H_{i} ) \cdot}( {Ip}_{i} )} - {{( H_{i} ) \cdot}( {Ip}_{i} )}} \rbrack/\lbrack {( {{( H_{i} )^{2}} + {( H_{i} )^{2}}} \rbrack,{\beta = {\frac{A^{T} \cdot B}{{A}^{2}}{Hp}_{i}{H_{i} \cdot ( {1 + {\Delta_{i} \cdot ( {j + {\beta \cdot \omega_{i}}} )}} )}}},} }$

where A is a vector, the first and second coordinates of which arerespectively formed by: A_(2i)=Δ_(i)·

(H_(i))·ω_(i) et A_(2i+1)=Δ_(i)·

(H_(i))·ω_(i),

B is a vector, the first and second coordinates of which arerespectively formed by:

B_(2i)=

(Ip_(i))−

(H_(i))+Δ_(i)·

(H_(i)) and B_(2i+1)=

(Ip_(i))−

(H_(i))−Δ_(i)·

(H_(i)), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i).

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the equation

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the field model is used to compute the prediction H_(i)        corresponding to the criterion C,

this computed prediction H_(i) being used for the following iterationuntil the computed criterion C becomes less than a prescribed non-zeropositive bound η.

A number of second embodiments are described below.

According to a second embodiment of the invention, at each iteration

-   -   the prediction H_(i) is initialized at the initial prescribed        values,    -   then the parameter β is computed so as to minimize the vector        A′·β+B′ on its coordinates, then the Δ_(i) and the disrupted        model Hp_(i) as a function of H_(i) and Ip_(i) according to the        equations:

$\Delta_{i} = \frac{{( {Ip_{i}} )} - {( H_{i} )}}{{( H_{i} )} + {( H_{i} )\beta \; \omega_{i}}}$Hp_(i) = H_(i) ⋅ (1 + Δ_(i) ⋅ (j + β ⋅ ω_(i)))

where A′ is a vector, the coordinates of which are respectively formedby: ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))],

B′ is a vector, the coordinates of which are respectively formed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))),

for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i),

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the equation

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the field model is used to compute the prediction H_(i)        corresponding to the criterion C,

this computed prediction H_(i) being used for the following iterationuntil the computed criterion C becomes less than a prescribed non-zeropositive bound η.

According to another second embodiment of the invention, at eachiteration

-   -   the prediction H_(i) is initialized at the initial prescribed        values,    -   then the parameter β is computed, then the Δ_(i) and the        disrupted model Hp_(i) as a function of H_(i) and Ip_(i)        according to the equations:

$\beta = \frac{A^{\prime \; T} \cdot B^{\prime}}{{A^{\prime}}^{2}}$$\Delta_{i} = \frac{{( {Ip_{i}} )} - {( H_{i} )}}{{( H_{i} )} + {( H_{i} )\beta \; \omega_{i}}}$Hp_(i) = H_(i) ⋅ (1 + Δ_(i) ⋅ (j + β ⋅ ω_(i)))

where A′ is a vector, the coordinates of which are respectively formedby: ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))],

B′ is a vector, the coordinates of which are respectively formed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))),

for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i),

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the equation

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the field model is used to compute the prediction H_(i)        corresponding to the criterion C,

this computed prediction H_(i) being used for the following iterationuntil the computed criterion C becomes less than a prescribed non-zeropositive bound η.

A number of third embodiments are described below.

According to a third embodiment of the invention, at each iteration

-   -   the prediction H_(i) is initialized at the prescribed initial        values,    -   the parameter β is then added as a state variable of the        Levenberg-Marquardt minimization algorithm,    -   then the Δ_(i) are computed as a function of H_(i) and Ip_(i)        and β according to the equations:

Hp _(i) =H _(i)·(1+Δ_(i)·(j+βω _(i))),

the Δ_(i) being a solution to the following system of equations:

(H _(i))−

(Ip _(i))+Δ_(i)·(

(H _(i))·β·ω_(i)−

(H _(i)))=0

and

(H _(i))−

(Ip _(i))+Δ_(i)·(

(H _(i))+

(H _(i))·β·ω_(i))=0

for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i),

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the equation

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the field model is used to compute the prediction H_(i)        corresponding to the criterion C,

this computed prediction H_(i) being used for the following iterationuntil the computed criterion C becomes less than a prescribed non-zeropositive bound η.

According to a third embodiment of the invention, at each iteration

-   -   the prediction H_(i) is initialized at the prescribed initial        values,    -   the parameter β is then added as a state variable of the        Levenberg-Marquardt minimization algorithm,    -   then the Δ_(i) are computed as minimizing a vector C·Δ-D over        its coordinates as a function of H_(i) and Ip_(i) and β        according to the equations:

Hp _(i) =H _(i)·(1+Δ_(i)·(j+·ω _(i))),

where Δ is a vector Δ having Δ_(i) as coordinates,

D is a vector, the first and second coordinates of which arerespectively formed by: −(

(H_(i))−

(Ip_(i))) and −(

(H_(i))−

(Ip_(i))),

C is a matrix, having as coefficients corresponding to Δ_(i)respectively

(H_(i))·β·ω_(i)−

(H_(i)) and

(H_(i))+

(H_(i))·β·ω_(i) and the coefficients 0 elsewhere, for i ranging from 1to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i),

-   -   then the error E_(i) is computed,    -   then the criterion C is computed according to the equation

${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$

-   -   then the field model is used to compute the prediction H_(i)        corresponding to the criterion C,        this computed prediction H_(i) being used for the following        iteration until the computed criterion C becomes less than a        prescribed non-zero positive bound η.

According to an embodiment of the invention, the determined frequenciesω_(i) are separate from one another.

According to an embodiment of the invention, the transmitter comprises aplurality of transmitter coils respectively transmitting a plurality oftransmitting magnetic fields,

the measuring device measuring for each receiver coil a plurality ofreceiving magnetic fields respectively induced by the plurality oftransmitting magnetic fields in the receiver coil and forming themeasurements Ip_(i) for i ranging from 1 to N.

According to another embodiment of the invention, the locator comprisesa transmitter coil transmitting at K different frequencies ω_(jk) and Jreceiver coils, the measuring device supplying the measurements Ip_(jk)for the index j ranging from 1 to J and the index k ranging from 1 to K,

the processing unit computes

$\rho_{j} = \frac{{\sum\limits_{k = 1}^{K}u_{jk}}{\cdot ( {{H_{jk}}^{2} + {{Ip}_{jk}}^{2} - {2 \cdot v_{jk}}} )}}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}$and$\beta = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jk} \cdot ( {v_{jk} - {H_{jk}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}}$with v_(jk) = (H_(jk))⋅(Ip_(jk)) + (H_(jk))⋅(Ip_(jk))u_(jk) = ((H_(jk))⋅(Ip_(jk)) − (H_(jk))⋅(Ip_(jk))) ⋅ ω_(jk)Ip_(jk) = H_(jk) ⋅ (1 + Δ_(jk) ⋅ (j + β ⋅ ω_(jk)))$\Delta_{\;^{jk}} = {\rho_{j}\frac{\omega_{jk}}{1 + ( {\beta \cdot \omega_{\;^{jk}}} )^{2}}}$

where H_(jk) is the prediction, ρ_(j) is the intensity of thedisruption, Hp_(jk) is the disrupted model and Hp_(jk)−Ip_(jk)=0.

According to another embodiment of the invention, the locator comprisesL transmitter coils or L transmitters, which transmit at K differentfrequencies ω_(jkl), and J receiver coils, the measuring devicesupplying the measurements Ip_(jkl) for the index j ranging from 1 to J,the index k ranging from 1 to K and the index 1 ranging from 1 to L,

the processing unit computes

$\rho_{jl} = \frac{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {{H_{jkl}}^{2} + {{Ip}_{jkl}}^{2} - {2 \cdot v_{jkl}}} )}}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}$and$\beta_{l} = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {v_{jkl} - {H_{jkl}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}}$with v_(jkl) = (H_(jkl))⋅(Ip_(jkl)) + (H_(jkl)) ⋅ (Ip_(jkl))u_(jkl) = ((H_(jkl)) ⋅ (Ip_(jkl)) − (H_(jkl))⋅(Ip_(jkl))) ⋅ ω_(jkl)Ip_(jkl) = H_(jkl) ⋅ (1 + Δ_(jkl) ⋅ (j + β ⋅ ω_(jkl)))$\Delta_{jkl} = {\rho_{j}\frac{\omega_{jkl}}{1 + ( {\beta \cdot \omega_{jkl}} )^{2}}}$

where H_(jkl) is the prediction, ρ_(jl) is the intensity of thedisruption, Hp_(jkl) is the disrupted model and Hp_(jkl)−Ip_(jkl)=0.

A second subject of the invention is a magnetic locator comprising:

-   -   at least one transmitter comprising at least one transmitter        coil and at least one generator able to generate at least one        transmission signal, connected to the at least one transmitter        coil, so that the at least one transmitter coil is able to        transmit at least one transmitting magnetic field at at least        one determined frequency ω_(i) in response to the transmission        signal that is sent to it by the generator,    -   at least one receiver comprising at least one receiver coil and        a measuring device, which is able to be connected to the at        least one receiver coil and which is able to supply at least one        measurement Ip_(i) of a receiving magnetic field respectively        induced by the transmitting magnetic field in each receiver        coil, to supply several measurements Ip_(i) for i ranging from 1        to N,    -   a processing unit comprising a field model making it possible to        compute a position and/or an orientation of the receiver by        computing a prediction H_(i) of the measurements as a function        of a criterion computed as a function of an error E_(i), itself        computed with respect to the measurements Ip_(i),

characterized in that

the processing unit is configured so that the error E_(i) is computed bysuccessive iterations from prescribed initial values of the predictionH_(i) as being the difference between the measurements Ip_(i) and adisrupted model Hp_(i) of the measurements, according to the equation

E _(i) =Ip _(i) −Hp _(i),

the disrupted model Hp_(i) of the measurements verifying the followingequations

${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{JH_{i}}{H_{i}}e^{{j\alpha}_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$

where P_(i) is a disruption made to the measurements Ip_(i) by amagnetic-field-disrupting material, ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material, β being a parameter of themagnetic-field-disrupting material,

the parameter β being identical for all the measurements Ip_(i),

the processing unit being configured to carry out the computation insuch a way as to minimize the criterion.

The locator may be produced according to several embodiments, where theprocessing unit is configured to implement the steps of respectivelyeach embodiment described above of the method at each iteration.

A third subject of the invention is a computer program, comprising codeinstructions for implementing the method for compensating a magneticlocator in the presence of at least one magnetic-field-disruptingmaterial, as described above, when the computer program is executed on acalculator.

The invention will be better understood on reading the followingdescription, given solely by way of non-limiting example with referenceto the appended drawings, wherein:

FIG. 1 schematically represents a modular block diagram of a magneticlocator according to an embodiment of the invention,

FIG. 2 schematically represents a magnetic-field-disrupting material,

FIGS. 3, 4 and 5 schematically represent three magnetic phase diagramsfor three different materials,

FIGS. 6 and 7 are Fresnel diagrams representing the disruptedmeasurement and a disrupted model Hp_(i), used according to anembodiment of the invention,

FIG. 8 is a modular block diagram of a processing unit of the locatoraccording to an embodiment of the invention,

FIG. 9 is a modular block diagram of a processing unit of the locatoraccording to FIG. 8, using a first algorithm,

FIG. 10 is a modular block diagram of a processing unit of the locatoraccording to FIG. 8, using a second algorithm,

FIG. 11 is a modular block diagram of a processing unit of the locatoraccording to FIG. 8, using a third algorithm.

Below is a description, with reference to the figures, of a method forcompensating a magnetic locator and a device for compensating a magneticlocator.

In FIG. 1, a magnetic locator 1 or device 1 for magnetic locationcomprises one or more transmitters 10 and one or more receivers 20.

The transmitter 10 comprises a transmitter coil or a plurality (numberNe) of transmitter coils, for example E1, E2, E3, and a generator or aplurality of generators, for example 101, 102, 103, of at least onetransmission signal, connected to the transmitter coils E1, E2, E3, tocontrol the transmitting coils with their respective transmissionsignal. The transmitter coils are rigidly attached to one and the samemechanical support of the transmitter 10, in order to occupy a knownposition and have a known orientation and can for example be orientedalong separate axes. The transmitter 10 has for example a known positionand a known orientation. Here, by way of non-limiting example, the caseis considered of a system in which the transmitter 10 comprises 3transmitter coils E1, E2, E3 oriented along three separate axes, forexample along the three axes of an orthonormal reference frame. Thesethree axes of the respective magnetic moments of the coils E1, E2, E3can be colinear with the axis of the winding of the coils in the case ofa coil orthogonal to the axis of winding. They can however be differenttherefrom if the coil is not at 90°, for example at 45°. When a voltageis imposed across the terminals of a transmitter coil E1, E2, E3, acurrent circulates in the transmitter coil E1, E2, E3 which thengenerates a magnetic field Be1, Be2, Be3 proportional to the currentthrough it and the shape of which depends on the features of the coil(orientation, magnetic moment, shape etc.). A voltage source may, forexample, be used as a generator 101, 102, 103 to impose a voltage acrossthe terminals of the transmitter coil E1, E2, E3 driving the creation ofa current.

When each generator 101, 102, 103 is started and connected to thetransmitter coil E1, E2, E3 respectively, each transmitter coil E1, E2,E3 transmits a transmitting magnetic field, Be1, Be2, Be3 respectively,in response to the transmission signal that is sent to it by thegenerator 101, 102, 103. The transmission signal and the transmittingmagnetic field, Be1, Be2, Be3 respectively, are for example sinusoidaland have for example a determined frequency, f1, f2, f3 respectively.The determined frequencies may be identical to one another or differentfrom one another. The determined frequencies may for example be of 100Hz to 50 kHz.

The receiver 20 comprises a receiver coil or several (number Nr)receiver coils, for example R1, R2, R3, and a measuring device 21, whichis connected to the receiver coils R1, R2, R3. The number Nr of receivercoils may be different from or equal to the number Ne of transmittercoils. The receiver coils are rigidly attached to one and the samemechanical support of the receiver 120 and may for example be orientedalong separate axes. The receiver 20 has for example a known positionand a known orientation. Here, by way of example, the case is consideredof a system in which the receiver 20 comprises 3 receiver coils R1, R2,R3 oriented along three separate axes, for example along the three axesof an orthonormal frame of reference. These three axes of the respectivemagnetic moments of the coils R1, R2, R3 may be colinear with the axisof the winding of the coils in the case of a coil orthogonal to the axisof winding. They may however be different therefrom if the coil is notat 90°, for example at 45°. In the presence of a variable magneticfield, a voltage (measurement) proportional to the variation of the fluxof the magnetic field appears in the receiver coil. By measuring thevoltage across the terminals of the receiver coil, for example using avoltmeter or other similar means, or by measuring the current(measurement) flowing through the receiver coil, for example by anampermeter or other similar means, it is possible to determine themagnetic field to which the receiver coil is subjected, on the conditionthat the features of the receiver coil, which particularly comprise themagnetic moment of the receiver coil, are known.

The measuring device 24 measures for each receiver coil R1, R2, R3 aplurality of receiving magnetic fields respectively induced by theplurality of transmitting magnetic fields Be1, Be2, Be3 and calledmeasurements Ip_(i) for i ranging from 1 to N and comprises for examplefor this purpose measuring modules 21, 22, 23 respectively connected tothe receiver coils R1, R2, R3. We have N=Nr·Ne possible pairs oftransmitter coils and receiver coils, which makes it possible toconstitute N measurements Ip_(i) by the measuring device 24. Accordingto an embodiment, N is greater than 1. The measurements Ip_(i) are forexample complex, each having a gain and a phase. The measurements Ip_(i)are for example supplied on a demodulation output of the measuringdevice 24. In the case where the transmission signal is sinusoidal witha determined frequency, the corresponding measurement Ip_(i) is alsosinusoidal with the same determined frequency. Thus, in the example ofFIG. 1, the measuring device 21 measures via the measuring module 21connected to the receiver coil R1:

-   -   the receiving magnetic field Br11 (written E1→R1), which is        induced in the receiver coil R1 by the transmitting magnetic        field Be1 of the transmitter coil E1,    -   the receiving magnetic field Br21 (written E2→R1), which is        induced in the receiver coil R1 by the transmitting magnetic        field Be2 of the transmitter coil E2,    -   the receiving magnetic field Br31 (written E3→R1), which is        induced in the receiver coil R1 by the transmitting magnetic        field Be3 of the transmitting coil E1.

The measuring device 21 measures via the measuring module 23 connectedto the receiver coil R2:

-   -   the receiving magnetic field Br12 (written E1→R2), which is        induced in the receiver coil R2 by the transmitting magnetic        field Be1 of the transmitter coil E1,    -   the receiving magnetic field Br22 (written E2→R2), which is        induced in the receiver coil R2 by the transmitting magnetic        field Be2 of the transmitter coil E2,    -   the receiving magnetic field Br32 (written E3→R2), which is        induced in the receiver coil R2 by the transmitting magnetic        field Be3 of the transmitter coil E1.

The measuring device 21 measures for the measuring module 22 connectedto the receiver coil R3:

-   -   the receiving magnetic field Br13 (written E1→R3), which is        induced in the receiver coil R3 by the transmitting magnetic        field Be1 of the transmitter coil E1,    -   the receiving magnetic field Br23 (written E2→R3), which is        induced in the receiver coil R3 by the transmitting magnetic        field Be2 of the transmitter coil E2,    -   the receiving magnetic field Br33 (denoted E3→R3), which is        induced in the receiver coil R3 by the transmitting magnetic        field Be3 of the transmitter coil E1.

The transmitter 10 and the receiver 20 are connected to a processingunit 25, (which can for example comprise a microprocessor) connected onthe one hand to the generator 101, 102, 103 of the transmitting device10 and on the other hand to the measuring device 24 of the receivingdevice 20. The processing unit 25 is configured to process thetransmission signals transmitted and the measurements Ip_(i) received,and thus makes it possible to retrieve from these transmittedtransmission signals and from these measurements Ip_(i) the position Pand the orientation Q of the receiver 20 relative to the transmitter 10.The processing unit 25 receives information concerning the features ofthe transmission signals applied to the transmitter coils as well asinformation concerning the features of the signals flowing through thereceiver coils (representative of the receiving magnetic field by thereceiver coil and therefore the measurements Ip_(i)). Based on theintensity and the phase of the receiving magnetic fields sensed by thereceiver coils, the processing unit 25 determines the spatialcoordinates of position P and orientation Q of all the receiver coilswith respect to all the transmitter coils, for example using aminimization algorithm, for example of Levenberg-Marquardt type, makingit possible to minimize the error between the measured fields (receivingmagnetic fields or measurements Ip_(i)) and the theoretical magneticfields modelled on the basis of a priori knowledge about the transmitterand the receiver.

A magnetic-field-disrupting material 3 can be present near the locator1, for example between the transmitter 10 and the receiver 20 or nearthem, as represented in FIG. 2, where only a transmitter coil of thetransmitter 10 and a receiver coil of the receiver 20 have beenrepresented by way of example. The disruptive material 3 may be forexample an electrically conductive material, for example metal. Anyelectrically conductive material 3 placed in a variable magnetic fieldgives rise to eddy currents in the conductive material 3, symbolized bythe current loops CF in FIG. 2. The eddy currents CF that then circulatein this conductor 3 in turn give rise to a disruptive magnetic field,the phase of which depends on the impedance of the conductor 3. But thisphase is constant for a given frequency. The disruptive material 3 canfor example be a metal prosthesis, such as for example a femoral head ofa hip prosthesis, a femoral stem of a hip prosthesis, a metal plate, forexample made of copper, another metal coil (other than the transmittercoils and the receiver coils) or other.

If the magnetic field induced by the disruptor is not in phase with thesignal of the transmitter then it is possible to detect the disruptionand to partly compensate for it. The outlined method makes it possibleto compensate for a single disruptor, it does not compensate fordisruptions in phase with the signal.

The situations can be summarized by the three phase diagrams of FIGS. 3,4 and 5 (real part Re of the magnetic fields on the abscissae, imaginarypart Im of the magnetic fields on the ordinates), with Bp the initialmagnetic field without disruption (for example the transmitting magneticfield Be1 or Be2 or Be3), Bs the magnetic field transmitted by the eddycurrents CF of the magnetic-field-disrupting material 3 and Bc theresulting magnetic field, equal to the sum of Bp and Bs.

In FIG. 3, in the case of a ferromagnetic material (such as for exampleferrites), the material generates a ferromagnetic disruption, wherethere are no eddy currents and there is no phase shift between theinitial field Bp and the resulting field Bc.

In FIG. 4, in the case of a magnetic-field-disrupting material 3, whichis electrically conductive (such as for example a copper and/or silverand/or aluminum plate), the eddy currents CF induced by the material 3create a secondary field Bs which has the effect of reducing the initialfield Bp and introducing a phase shift. The resulting field Bc isphase-shifted and lower in amplitude with respect to the initial fieldBp.

In FIG. 5, in the case of a magnetic-field-disrupting material 3, whichis mixed (both ferromagnetic and electrically conductive), forrelatively low frequencies, the ferromagnetic nature means that theamplitude of the resulting field Bc is higher than that of the initialfield Bp. The eddy currents CF induced by the material 3 at the sametime introduce a phase shift. As the frequency increases, the effect ofthe ferromagnetism decreases, that of the eddy currents CF induced bythe material 3 CF increases, the amplitude of the resulting field Bcdecreases more and more, the phase shift increases then decreasesaccording to a law specific to the material 3.

The invention makes it possible to compensate for the disruption Bs dueto the eddy currents CF induced by the material 3. The ferromagneticdisruptions are assumed to be zero.

The magnetic-field-disrupting material 3 can be a conductive metalobject at a certain position in space in relation to a transmitter coil.This implies that if the metal object moves, it constitutes a newdisruptor, the features of which are different.

The magnetic locator 1 implements the method for compensating for thepresence of the magnetic-field-disrupting material 3, described below.

In FIG. 8, the locator 1 comprises the processing unit 25 comprising amodule 26 for modelling the field making it possible to compute aposition P and/or an orientation Q of the receiver 20 by computing aprediction H_(i) of the measurements as a function of a criterion C ofminimization of an error E_(i) computed with respect to the measurementsIp_(i). This module 26 may for example comprise a Kalman filter forcomputing the prediction H_(i). The module 26 disposes of a physicalmodel of the locator 1, which predicts in the absence of disruption andas a function of the position P and/or the orientation Q of the receiver20 the N measurements, to supply the predictions H_(i). The module 26searches for the position P and/or the orientation Q (or state of thesensor P, Q) and computes the prediction H_(i) verifying the criterionC. The criterion C is considered by the module 26 as representing thedeviation (which can for example be a norm of the error taken in themeaning of L2, which can be the sum of the squares of the errors E_(i)over i ranging from 1 to N) between the prediction H_(i) and themeasurements Ip_(i). The criterion C can be computed as being forexample a norm of the error E_(i) taken in the meaning of L². Accordingto an embodiment, the criterion C can be computed as being the sum ofthe squares of the errors E_(i) over i ranging from 1 to N. According toan embodiment, the criterion C can be computed according to thefollowing equation

$C = {\sum\limits_{i = 0}^{N}{{{H_{i}( {P,Q} )} - {IP}_{i}}}^{2}}$

According to an embodiment, the error E_(i) is computed by an errorcomputing module 27 as being the difference between the measurementsIp_(i) and a disrupted model Hp_(i) of the measurements, according tothe equation

E _(i) =Ip _(i) −Hp _(i).

At a given instant, there are N complex measurements Ip_(i) and Ncomplex predictions H_(i) resulting from the model 26, for i rangingfrom 1 to N. Each of these measurements Ip_(i) is made at a certainfrequency or angular frequency (equal to the frequency multiplied by2π), which is written below ω_(i).

The measurements Ip_(i) are for example stored in a vector Ip having ascoordinates these measurements Ip_(i), i.e.

${Ip} = {\begin{pmatrix}{{Br}\; 11} \\{{Br}\; 21} \\\ldots \\\frac{{BrN}_{r}1}{{Br}\; 21} \\\ldots \\\ldots \\{{BrN}_{e}N_{r}}\end{pmatrix} = \begin{pmatrix} {E\; 1}arrow{R\; 1}  \\ {E\; 1}arrow{R\; 2}  \\\ldots \\\frac{ {E\; 1}arrow R_{N_{r}} }{ {E\; 2}arrow{R\; 1} } \\\ldots \\\ldots \\ E_{N_{e}}arrow R_{N_{r}} \end{pmatrix}}$

The predictions H_(i) are for example stored in a vector H(P,Q) havingas coordinates these predictions H_(i), i.e.

${H( {P,Q} )} = {\begin{pmatrix}{H( {{Br}\; 11} )} \\{H( {{Br}\; 21} )} \\\ldots \\\frac{H( {{BrN}_{r}1} )}{H( {{Br}\; 21} )} \\\ldots \\\ldots \\{H( {{BrN}_{e}N_{r}} )}\end{pmatrix} = \begin{pmatrix}{H( {E\; 1}arrow{R\; 1} )} \\{H( {E\; 1}arrow{R\; 2} )} \\\ldots \\\frac{H( {E\; 1}arrow R_{N_{r}} )}{H( {E\; 2}arrow{R\; 1} )} \\\ldots \\\ldots \\{H( E_{N_{e}}arrow R_{N_{r}} )}\end{pmatrix}}$

In the absence of any magnetic-field-disrupting material 3 by eddycurrent P_(i)=0, it is supposed that the model 26 is appropriatelycalibrated and that it is correctly following the measurement (thencalled I_(i) in the absence of any magnetic-field-disrupting material 3)as a function of the time t, according to the equationH_(i)(t)=I_(i)(t)+ε_(i) with ε_(i) negligible (ε_(i)=0 in the remainderof the text).

When a magnetic-field-disrupting material 3 is present, a disruptionP_(i), non-negligible, is added to the measurement I_(i) and this thengives Ip_(i)=I_(i)+P_(i) and the disrupted model Hp_(i) is equal toHp_(i)=H_(i)+P_(i). FIG. 6 is a Fresnel diagram representing thedisrupted measurement Ip_(i) with respect to a non-disrupted measurementI_(i). FIG. 7 is a Fresnel diagram representing the non-disruptedprediction H_(i) with respect to the disrupted model Hp_(i).

No correction is made to the measurement Ip_(i) which is itselfaccurate, but the disruption P_(i) is modeled by computing a disruptedmodel Hp_(i) such that the criterion C is minimal. According to anembodiment, the processing unit 25 comprises a module 29 for computingthe criterion C of minimization of an error E_(i) computed with respectto the measurements Ip_(i). According to an embodiment,

$C = {\sum\limits_{i = 0}^{N}{{{HP}_{i} - {IP}_{i}}}^{2}}$

According to an embodiment, one computes as disrupted model Hp_(i) aprojection of the prediction H_(i) onto the measurements Ip_(i) as afunction of a parameter β characteristic of themagnetic-field-disrupting material 3, and for example only as a functionof the parameter β. This projection makes it possible to reduce theeffect of the magnetic-field-disrupting material 3 by eddy currents.

According to an embodiment, the criterion C=E^(T)·E is minimized

with E=Ip−Hp(H,Ip,β).

The vector Hp(H,Ip,β) is a projection function of H onto Ip and iscomputed as a function of the vector H(P, Q) and of the vector Ip.

The vector Hp(H,Ip,β) has as coordinates this disrupted model Hp_(i),for i ranging from 1 to N, i.e.

${{Hp}( {H,{Ip},\beta} )} = {\begin{pmatrix}{{Hp}( {{Br}\; 11} )} \\{{Hp}( {{Br}\; 21} )} \\\ldots \\\frac{{Hp}( {{BrN}_{r}1} )}{{Hp}( {{Br}\; 21} )} \\\ldots \\\ldots \\{{Hp}( {{BrN}_{e}N_{r}} )}\end{pmatrix} = \begin{pmatrix}{{Hp}( {E\; 1}arrow{R\; 1} )} \\{{Hp}( {E\; 1}arrow{R\; 2} )} \\\ldots \\\frac{{Hp}( {E\; 1}arrow R_{N_{r}} )}{{Hp}( {E\; 2}arrow{R\; 1} )} \\\ldots \\\ldots \\{{Hp}( E_{N_{e}}arrow R_{N_{r}} )}\end{pmatrix}}$

The disrupted model Hp_(i) of the measurements is computed by a module28 for computing the disrupted model based on the measurements Ip_(i)and the prediction H_(i) by the following equations:

$P_{i} = {\rho_{i}\frac{{jI}_{i}}{I_{i}}e^{j\; \alpha_{i}}}$I_(i) = H_(i) = Ip_(i) − P_(i)

where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material 3, ρ_(i) is the intensity of thedisruption P_(i), α_(i) is a phase shift angle caused by themagnetic-field-disrupting material 3 in the disruption P_(i).

The phase shift angles α_(i) are related by the relationshipcharacteristic of the magnetic-field-disrupting material 3 according tothe equation

α_(i)=−arctan(β·ω_(i)).

where β is a parameter characteristic of the magnetic-field-disruptingmaterial 3.

The parameter β is computed as being identical for all the measurementsIp_(i) and represents a ratio of an inductance L_(p) modelling thedisruptive material 3 to a resistance R_(p) modelling the disruptivematerial 3 in a certain position relative to the transmitter 10, theimpedance of the disruptive material 3 being Zp=R_(p)+j·L_(p)·ω_(i).

The disruption P_(i) and/or the intensity ρ_(i) of the disruption P_(i)and/or the phase shift angle α_(i) and/or the parameter β and/or thedisrupted model Hp_(i) is computed in such a way as to minimize theerror E_(i).

The vector projection function Hp(H,Ip,β) is modeled to identify theparameter β.

For i ranging from 1 to N, N equations are to be solved.

Supposing that I_(i)=H_(i) and Ip_(i)=Hp_(i), this gives

H _(i) +P _(i) −Ip _(i)=0

then the projected model vector Hp is obtained, the coordinates of whichare Hp_(i) given by the following equation:

Hp_(i) = H_(i) ⋅ (1 + Δ_(i) ⋅ (j + β ⋅ ω_(i))) with$\Delta_{i} = \frac{\rho_{i}}{{H_{i}} \cdot \sqrt{{\beta^{2} \cdot \omega_{i}^{2}} + 1}}$

Δ_(i) is called the projection distance.

The disruption P_(i) and/or the intensity ρ_(i) of the disruption P_(i)and/or the phase shift angle α_(i) and/or the parameter β and/or thedisrupted model Hp_(i) and/or the projection distance Δ_(i) can becomputed by the processing unit 25 by a computing method usingsuccessive iterations according to one of FIGS. 8 to 11. For example,according to an embodiment, at each iteration

-   -   the predictions H_(i) of the module 26 are initialized at given        values,    -   then the module 28 is used to compute by one of the described        computing methods or algorithms the disrupted model Hp_(i), as a        function of H_(i) and Ip_(i), for example according to the        equations

Δ_(i)=[

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i))]/[(

(H _(i))²+

(H _(i))²]

β=[−

(H _(i))²−

(H _(i))²+

(H _(i))·

(Ip _(i))+

(H _(i))·

(Ip _(i))]/[(

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i)))·ω_(i)],

Hp _(i) =H _(i)·(1+Δ_(i)·(j+β·ω _(i))),

-   -   then the module 27 is used to compute the error E_(i) according        to the equation

E _(i) =Ip _(i) −Hp _(i),

-   -   then the module 29 is used to compute the criterion C according        to the equation

${C = {\sum\limits_{i = 0}^{N}{{{HP}_{i} - {IP}_{i}}}^{2}}},$

or according to the equation

$C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}$

-   -   then the model of the module 26 is used to compute the        prediction H_(i) corresponding to the criterion C using the        minimization algorithm, for example of Levenberg-Marquardt type,        of the model. This minimization algorithm searches via the        module 26 for the position P and/or the orientation Q of the        receiver 20 which minimizes the deviation between the prediction        H_(i) according to the criterion C and the measurements Ip_(i).        The prediction H_(i) thus computed by the model 26 is used for        the following iteration. The iterations are continued until, for        example, the computed criterion C becomes less than a prescribed        non-zero positive bound η.

In the case where the disruptive material 3 is moving with respect tothe transmitter 10 and/or the receiver 20, the parameter β varies overtime as a function of the movement of the disruptive material 3.

Each module 26, 27, 28, 29 of the processing unit 25 and/or each step ofthe method can be implemented by computing means, for example by one ormore calculator(s), one or more computers, one or more microprocessorsand one or more computer programs. The computer program(s) comprise codeinstructions for implementing the compensating method.

According to an embodiment, the magnetic locator 1 comprising:

-   -   at least one transmitter 10 comprising a plurality (Ne) of        transmitter coils and a generator able to generate at least one        transmission signal, connected to the transmitter coils, so that        each transmitter coil is able to transmit at least one        transmitting magnetic field at at least one determined frequency        ω_(i) in response to the transmission signal that is sent to it        by the generator,    -   at least one receiver comprising one or more (Nr) receiver coils        and a measuring device, which is able to be connected to the        receiver coil or coils and which is able to measure for each        receiver coil a plurality of receiving magnetic fields        respectively induced by the plurality of transmitting magnetic        fields and called measurements Ip_(i) for i ranging from 1 to N,    -   a processing unit 25 comprising a field model making it possible        to compute a position P and/or an orientation Q of the receiver        by computing the prediction H_(i) of the measurements as a        function of the criterion C computed as a function of the error        E_(i), itself computed with respect to the measurements Ip_(i),

characterized in that

the processing unit 25 is configured so that the error E_(i) is computedby successive iterations from initial prescribed values of theprediction H_(i) as being the difference between the measurements Ip_(i)and a disrupted model Hp_(i) of the measurements, according to theequation

E _(i) =Ip _(i) −Hp _(i),

the disrupted model Hp_(i) of the measurements verifying the followingequations

${{Hp}_{i} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$

where P_(i) is a disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material 3, ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material 3, being a parameter of themagnetic-field-disrupting material 3,

the parameter β being identical for all the measurements Ip_(i),

the processing unit 25 being configured to carry out the computation insuch a way as to minimize the criterion C.

The processing unit 25 is thus configured to compensate for the presenceof the magnetic-field-disrupting material 3.

The magnetic locator 1 thus comprises in its processing unit 25 meansfor compensating for the presence of the magnetic-field-disruptingmaterial 3.

Below is a description of a first algorithm for carrying out thecomputation, with reference to the FIG. 9.

According to an embodiment, starting from the equation

H_(i)−Ip_(i)+Δ_(i)·H_(i)·(j+β·ω_(i)))=0, one obtains on the real partsand the imaginary parts thereof a system of two equations, which gives aunique solution for Δ_(i) and β, namely the solution

Δ_(i)=[

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i))]/[(

(H _(i))²+

(H _(i))²]

and

β=[−

(H _(i))²−

(H _(i))²+

(H _(i))·

(Ip _(i))+

(H _(i))·

(Ip _(i))]/[(

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i)))·ω_(i)]

According to an embodiment, the first computing algorithm A makesprovision for to be computed as being a solution to the following systemof equations, resulting from the preceding equations giving Hp_(i),namely

Δ_(i)·

(H _(i))·β·ω_(i)=

(Ip _(i))−

(H _(i))+Δ_(i)·

(H _(i))

and

Δ_(i)·

(H_(i))·β·ω_(i)=

(Ip_(i))−

(H_(i))−Δ_(i)·

(H_(i))for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i) and is also written

(H_(i)),

(H_(i)) is the imaginary part of the prediction H_(i) and is alsowritten ℑ(H_(i)),

(Ip_(i)) is the real part of the measurement Ip_(i) and is also written

(IP_(i))

(Ip_(i)) is the imaginary part of the measurement Ip_(i) and is alsowritten ℑ(IP_(i)).

According to an embodiment, this first computing algorithm A can makeprovision for the parameter to be computed as minimizing a vector A·β−Bover its coordinates, where

A is a vector, the first and second coordinates of which arerespectively formed by: Δ_(i)·

(H_(i))·ω_(i) and Δ_(i)·

(H_(i))·ω_(i), B is a vector, the first and second coordinates of whichare respectively formed by:

(Ip_(i))−

(H_(i))+Δ_(i)·

(H_(i)) and

(Ip_(i))−

(H_(i))−Δ_(i)·

(H_(i)).

In an embodiment, the parameter β can be computed as minimizing the sumof the squares of the coordinates of the vector A·β−B for i ranging from1 to N.

In another embodiment, the parameter β can be computed as being aminimal solution to the vector equation A·β=B, by

$\beta = \frac{A^{T} \cdot B}{{A}^{2}}$

The operator ^(T) denotes transposition.

In another embodiment, a weighting matrix denoted W is used such that:

(W·A)·β=(W·B)

with W=P·I

and P=(p ₁ ,p ₂ ,p ₃ , . . . ,p _(N)).

The parameter β can then be computed as being

$\beta = \frac{( {W \cdot A} )^{T} \cdot B}{{( {W \cdot A} )}^{2}}$

For example, the p_(i) can be equal to a power of the norm of the H_(i),i.e.

P=(|H ₀|^(k) ,|H ₁|^(k) , . . . ,|H _(N)|^(k)).

Thus, the greater k is, the more the large measurements are taken intoaccount, in relation to the small ones. k=2 seems to be a goodcompromise. This avoids the small values of the coordinates of thevectors A and B leading to erroneous phases and in the estimating of βthey can be rejected more often.

In an embodiment, this first computing algorithm A can be implemented bythe following steps:

-   -   computing Δ_(i) according to the equation Δ_(i)=[        (H_(i))·        (Ip_(i))−        (H_(i))·        (Ip_(i))]/[(        (H_(i))²+        (H_(i))²],    -   computing β according to the equation

${\beta = {{\frac{A^{T} \cdot B}{{A}^{2}}\mspace{14mu} {or}\mspace{14mu} \beta} = \frac{( {W \cdot A} )^{T} \cdot B}{{( {W \cdot A} )}^{2}}}},$

computing Hp_(i) according to the equationHp_(i)=H_(i)·(1+Δ_(i)·(j+β·ω_(i))), as represented in FIG. 9.

Below is a description of a second computing algorithm, with referenceto FIG. 10.

According to an embodiment, starting from the equation

H _(i) −Ip _(i)+Δ_(i) ·H _(i)·(j+β·ω _(i)))=0,

one obtains on the real parts and the imaginary parts thereof a systemof two equations, which gives a unique solution for Δ_(i) and, namelythe solution

Δ_(i)=[

(Ip _(i))−

(H _(i))]/[

(H _(i))+

(H _(i))·β·ω_(i)]

According to an embodiment, the second computing algorithm B makesprovision for to be computed as being a solution to the followingequation, resulting from the preceding equation giving Δ_(i), namelyβ·ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))]+

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i)))=0 for i ranging from 1 to N.

According to an embodiment, this second computing algorithm B can makeprovision for the parameter to be computed as minimizing a vectorA′·β+B′ over its coordinates, where

A′ is a vector, the coordinates of which are respectively formed by:ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))],

B′ is a vector, the coordinates of which are respectively formed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))).

In an embodiment, the parameter β can be computed as minimizing the sumof the squares of the coordinates of the vector A′·β+B′ for i rangingfrom 1 to N.

In another embodiment, the parameter β can be computed as being aminimal solution to the vector equation A′·β=−B′, by

$\beta = \frac{A^{\prime T} \cdot B^{\prime}}{{A^{\prime}}^{2}}$

In an embodiment, this second computing algorithm B can be implementedby the following steps:

-   -   computing the vectors A′ and B′ according to the coordinates        indicated above,    -   computing β according to the equation

$\beta = \frac{A^{\prime T} \cdot B^{\prime}}{{A^{\prime}}^{2}}$

or according to the equation

$\beta = \frac{( {W \cdot A^{\prime}} )^{T} \cdot B^{\prime}}{{( {W \cdot A^{\prime}} )}^{2}}$

if the aforementioned weighting matrix W is used,

-   -   computing Δ_(i) according to the equation Δ_(i)=[        (Ip_(i))−        (H_(i))]/[        (H_(i))+        (H_(i))·β·ω_(i)] and computing Hp_(i) according to the equation        Hp_(i)=H_(i)·(1+Δ_(i)·(j+P·ω_(i))), as represented in FIG. 10.

Below is a description of a third computing algorithm C, with referenceto FIG. 11.

According to an embodiment, starting from the equation

H _(i) −Ip _(i)+Δ_(i) ·H _(i)·(j+β·ω _(i)))=0,

one obtains on the real parts and the imaginary parts thereof a systemof two equations namely

(H _(i))−(Ip _(i))+Δ_(i)·(

(H _(i))·β·ω_(i)−

(H _(i)))=0

and

(H _(i))−

(Ip _(i))+Δ_(i)·(

(H _(i))+

(H _(i))·β·ω_(i))=0

According to an embodiment, the third computing algorithm C makesprovision for β to be computed as being a solution to this system ofequations. For example the Levenberg-Marquardt algorithm, which producesthe inverse solution, also computes the parameter β as being a statevariable.

According to an embodiment, this third computing algorithm C can makeprovision for a vector Δ having Δ_(i) as coordinates to be computed asminimizing a vector C·Δ−D over its coordinates, where

D is a vector, the first and second coordinates of which arerespectively formed by: −(

(H_(i))−

(Ip_(i))) and −(

(H_(i))−

(Ip_(i))),

C is a matrix, having as coefficients corresponding to the Δ_(i)respectively

(H_(i))·β·ω_(i)−

(H_(i)) and

(H_(i))+

(H_(i))·β·ω_(i), i.e. the vector C·Δ−D is equal to:

$\begin{pmatrix}( & 0 & \ldots & 0 \\( {{{( H_{0} )} + {( H_{0} )}}{\cdot \beta \cdot \omega_{0}}} ) & 0 & \ldots & 0 \\0 & ( & \ldots & 0 \\0 & ( {{{( H_{1} )} + {( H_{1} )}}{\cdot \beta \cdot \omega_{1}}} ) & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots \\0 & 0 & \ldots & ( \\0 & 0 & \ldots & ( {{{( H_{N} )} + {( H_{N} )}}{\cdot \beta \cdot \omega_{N}}} )\end{pmatrix}\begin{pmatrix}\Delta_{0} \\\Delta_{1} \\\ldots \\\Delta_{N}\end{pmatrix}\begin{pmatrix}{{( {IP}_{0} )} - {( H_{0} )}} \\{{( {IP}_{0} )} - {( H_{0} )}} \\{{( {IP}_{1} )} - {( H_{1} )}} \\{{( {IP}_{1} )} - {( H_{1} )}} \\\ldots \\\ldots \\{{( {IP}_{N} )} - {( H_{N} )}} \\{{( {IP}_{N} )} - {( H_{N} )}}\end{pmatrix}$

In another embodiment, the parameter β can be computed as being asolution to the vector equation C·Δ=D. For example, a matrix C⁺ iscomputed which is the pseudoinverse of C, to compute the vector Δ asbeing Δ=C⁺·D.

In an embodiment, this third computing algorithm C can be implemented bythe following steps:

-   -   estimating the parameter β via the Levenberg-Marquardt        algorithm,    -   computing the matrix C and the vector D, computing the vector Δ        verifying the equation C·Δ=D, for example by Δ=C⁺·D    -   computing Hp_(i) according to the equation        Hp_(i)=H_(i)·(1+Δ_(i)·(j+P·ω_(i))), as represented in FIG. 11.

Below is a description of a variant of the compensating method anddevice according to the invention. According to this variant, eachtransmitter coil transmits several frequencies. Thus several frequenciesare transmitted per transmitter coil axis. It can thus be consideredthat the magnetic-field-disrupting material 3 constitutes severalmagnetic-field-disrupting materials 3 and that the projection distancesare linked for the different frequencies. It is for example possible toconsider a locator 1 having a transmitter coil transmitting at Kdifferent frequencies and J receiver coils, with K greater than or equalto 2 and J greater than or equal to 2. This gives N=K·J measurementsIp_(i). This gives N equations of the form:

Ip _(i) =H _(i)·(1+Δ_(i)·(j+β·ω _(i))).

It is possible to break down the index i belonging to [1, N] into twoindices j belonging to [1, J] and k belonging to [1, K]. The precedingequation then becomes:

Ip _(jk) =H _(jk)·(1+Δ_(jk)·(j+β·ω _(jk))).

In all the equations, the letter j not appearing in the index is thecomplex number, the square of which is equal to −1, as is known to thoseskilled in the art.

The change of variable is set:

$\Delta_{\;^{jk}} = {\rho_{J}\frac{\omega_{jk}}{1 + ( {\beta \cdot \omega_{\;^{jk}}} )^{2}}}$

ρ_(j) depends only on j.

The equations to be minimized become:

$F_{({\rho_{j},\beta})} = \{ \begin{matrix}\begin{matrix}{R_{jk} = {{( H_{jk} )} - {( {Ip}_{jk} )} + {\rho_{j}{\frac{\omega_{jk}}{1 + ( {\beta {\cdot \omega_{jk}}} )^{2}} \cdot}}}} \\{( {{{( H_{jk} ) \cdot \beta \cdot \omega_{jk}}} - {( H_{jk} )}} ) = 0}\end{matrix} \\\begin{matrix}{I_{jk} = {{( H_{jk} )} - {( {Ip}_{jk} )} + {\rho_{j}{\frac{\omega_{jk}}{1 + ( {\beta {\cdot \omega_{jk}}} )^{2}} \cdot}}}} \\{( {{{( H_{jk} ) \cdot \beta \cdot \omega_{jk}}} + {( H_{jk} )}} ) = 0}\end{matrix}\end{matrix} $

This gives a system of 2JK equations with J+1 unknowns to be minimized.

According to an embodiment, 2·J·K≥J+1.

Solving two by two obtains:

v _(jk)=

(H _(jk))·

(Ip _(jk))+ℑ(H _(jk))·ℑ(Ip _(jk))

u _(jk)=(

(H _(jk))·ℑ(Ip _(jk))−ℑ(H _(jk))·

(Ip _(jk)))·ω_(jk)

u _(jk)·ρ_(j) =|H _(jk)|² +|Ip _(jk)|²−2·v _(jk)

u _(jk) ·β=v _(jk) −|H _(jk)|²

The least squares solution is expressed by:

$\rho_{j} = \frac{\sum\limits_{k = 1}^{K}{u_{jk} \cdot ( {{H_{jk}}^{2} + {{Ip}_{jk}}^{2} - {2 \cdot v_{jk}}} )}}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}$and$\beta = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jk} \cdot ( {v_{jk} - {H_{jk}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}}$

If there are L transmitters 10 with L greater than or equal to 2, therewill be a third index l belonging to [l, L] and one parameter β_(l) issearched for per transmitter 10 _(l) according to the followingequations:

$\rho_{jl} = \frac{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {{H_{jkl}}^{2} + {{Ip}_{jkl}}^{2} - {2 \cdot v_{jkl}}} )}}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}$and$\beta_{l} = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {v_{jkl} - {H_{jkl}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}}$

In this case there are 2JKL measurements for L(J+1) unknowns. Accordingto an embodiment, 2·J·K·L≥L·(J+1).

It is found that increasing the number of frequencies per axis does notincrease the number of unknowns and therefore increases the redundancy.

Of course, the possibilities, embodiments, features, variants andexamples above can be combined with one another or be selectedindependently of one another.

1. A method for compensating a magnetic locator in the presence of atleast one magnetic-field-disrupting material, said magnetic locatorcomprising: at least one transmitter comprising at least one (Ne)transmitter coil (E1, E2, E3, . . . ) and at least one generator of atleast one transmission signal, connected to the at least one transmittercoil (E1, E2, E3, . . . ), so that the at least one transmitter coil(E1, E2, E3, . . . ) transmits at least one transmitting magnetic field(Be1, Be2, Be3, . . . ) at at least one determined frequency (o inresponse to the transmission signal that is sent to it by the generator,at least one receiver comprising at least one (Nr) receiver coil (R1,R2, R3, . . . ) and a measuring device, which is connected to the atleast one receiver coil (R1, R2, R3, . . . ) and which supplies at leastone measurement Ip_(i) of a receiving magnetic field (Br11, Br21, Br31;Br12, Br22, Br32; Br13, Br23, Br33, . . . ) respectively induced by thetransmitting magnetic field (Be1, Be2, Be3, . . . ) in each receivercoil (R1, R2, R3, . . . ), in such a way as to supply severalmeasurements Ip_(i) for i ranging from 1 to N, a processing unit (25)comprising a field model making it possible to compute a position (P)and/or an orientation (Q) of the receiver by computing a predictionH_(i) of the measurements as a function of a criterion (C) computed as afunction of an error E_(i), itself computed with respect to themeasurements Ip_(i), characterized in that the error E_(i) is computedby successive iterations from initial prescribed values of theprediction H_(i) as being the difference between the measurements Ip_(i)and a disrupted model Hp_(i) of the measurements, according to theequationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the computation being carried out insuch a way as to minimize the criterion (C), at each iteration theprediction H_(i) is initialized at the prescribed initial values, thenare computed Δ_(i), the parameter β so as to minimize the vector A·β−Bover its coordinates, and the disrupted model Hp_(i) as a function ofH_(i) and Ip_(i) according to the equationsΔ_(i)=[

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i))]/[

(H _(i))²+

(H _(i))²],Hp _(i) =H _(i)·(1+Δ_(i)·(j+βω _(i))), where A is a vector, the firstand second coordinates of which are respectively formed by:A_(2i)=Δ_(i)·

(H_(i))·ω_(i) and A_(2i+1)=Δ_(i)·

(H_(i))·ω_(i), B is a vector, the first and second coordinates of whichare respectively formed by:B _(2i)=

(Ip _(i))−

(H _(i))+Δ_(i)·

(H _(i))andB _(2i+1)=

(Ip _(i))−

(H _(i))−Δ_(i)·

(H _(i)), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound.
 2. A method for compensating a magnetic locatorin the presence of at least one magnetic-field-disrupting material, saidmagnetic locator comprising: at least one transmitter comprising atleast one (Ne) transmitter coil (E1, E2, E3, . . . ) and at least onegenerator of at least one transmission signal, connected to the at leastone transmitter coil (E1, E2, E3, . . . ), so that the at least onetransmitter coil (E1, E2, E3, . . . ) transmits at least onetransmitting magnetic field (Be1, Be2, Be3, . . . ) at at least onedetermined frequency (o in response to the transmission signal that issent to it by the generator, at least one receiver comprising at leastone (Nr) receiver coil (R1, R2, R3, . . . ) and a measuring device,which is connected to the at least one receiver coil (R1, R2, R3, . . .) and which supplies at least one measurement Ip_(i) of a receivingmagnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13, Br23, Br33, .. . ) respectively induced by the transmitting magnetic field (Be1, Be2,Be3, . . . ) in each receiver coil (R1, R2, R3, . . . ), in such a wayas to supply several measurements Ip_(i) for i ranging from 1 to N, aprocessing unit (25) comprising a field model making it possible tocompute a position (P) and/or an orientation (Q) of the receiver bycomputing a prediction H_(i) of the measurements as a function of acriterion (C) computed as a function of an error E_(i), itself computedwith respect to the measurements Ip_(i), characterized in that the errorE_(i) is computed by successive iterations from initial prescribedvalues of the prediction H_(i) as being the difference between themeasurements Ip_(i) and a disrupted model Hp_(i) of the measurements,according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the computation being carried out insuch a way as to minimize the criterion (C), at each iteration theprediction H_(i) is initialized at the prescribed initial values, thenare computed Δ_(i), the parameter β and the disrupted model Hp_(i) as afunction of H_(i) and Ip_(i) according to the equations$\Delta_{i} = {\lbrack {{( H_{i} )}{{\cdot ( {Ip}_{i} )} - {{( H_{i} ) \cdot}( {Ip}_{i} )}}} \rbrack/\lbrack {( {{( H_{i} )^{2}} + {( H_{i} )^{2}}} \rbrack,{\beta = {{\frac{A^{T} \cdot B}{{A}^{2}}{Hp}_{i}} = {H_{i} \cdot ( {1 + {\Delta_{i} \cdot ( {j + {\beta \cdot \omega_{i}}} )}} )}}},} }$where Δ is a vector, the first and second coordinates of which arerespectively formed by: A_(2i)=Δ_(i)·

(H_(i))·ω_(i) and A_(2i+1)=Δ_(i)·

(H_(i))·ω_(i), B is a vector, the first and second coordinates of whichare respectively formed by: B_(2i)=

(Ip_(i))−

(H_(i))+Δ_(i)·

(H_(i)) and B_(2i+1)=

(Ip_(i))−

(H_(i))−Δ_(i)·

(H_(i)), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 3. A method for compensating a magneticlocator in the presence of at least one magnetic-field-disruptingmaterial, said magnetic locator comprising: at least one transmittercomprising at least one (Ne) transmitter coil (E1, E2, E3, . . . ) andat least one generator of at least one transmission signal, connected tothe at least one transmitter coil (E1, E2, E3, . . . ), so that the atleast one transmitter coil (E1, E2, E3, . . . ) transmits at least onetransmitting magnetic field (Be1, Be2, Be3, . . . ) at at least onedetermined frequency (o in response to the transmission signal that issent to it by the generator, at least one receiver comprising at leastone (Nr) receiver coil (R1, R2, R3, . . . ) and a measuring device,which is connected to the at least one receiver coil (R1, R2, R3, . . .) and which supplies at least one measurement Ip_(i) of a receivingmagnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13, Br23, Br33, .. . ) respectively induced by the transmitting magnetic field (Be1, Be2,Be3, . . . ) in each receiver coil (R1, R2, R3, . . . ), in such a wayas to supply several measurements Ip_(i) for i ranging from 1 to N, aprocessing unit (25) comprising a field model making it possible tocompute a position (P) and/or an orientation (Q) of the receiver bycomputing a prediction H_(i) of the measurements as a function of acriterion (C) computed as a function of an error E_(i), itself computedwith respect to the measurements Ip_(i), characterized in that the errorE_(i) is computed by successive iterations from initial prescribedvalues of the prediction H_(i) as being the difference between themeasurements Ip_(i) and a disrupted model Hp_(i) of the measurements,according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the computation being carried out insuch a way as to minimize the criterion (C), at each iteration theprediction H_(i) is initialized at the prescribed initial values, thenare computed the parameter β so as to minimize the vector A′·β+B′ overits coordinates, then the Δ_(i) and the disrupted model Hp_(i) as afunction of H_(i) and Ip_(i) according to the equations:Δ_(i)−(

(Ip _(i))−

(H _(i)))/(

(H _(i))+

(H _(i))βω_(i)),Hp _(i) =H _(i)·(1+Δ_(i)·(j+βω _(i))), B′ is a vector, the coordinatesof which are respectively formed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 4. A method for compensating a magneticlocator in the presence of at least one magnetic-field-disruptingmaterial, said magnetic locator comprising: at least one transmittercomprising at least one (Ne) transmitter coil (E1, E2, E3, . . . ) andat least one generator of at least one transmission signal, connected tothe at least one transmitter coil (E1, E2, E3, . . . ), so that the atleast one transmitter coil (E1, E2, E3, . . . ) transmits at least onetransmitting magnetic field (Be1, Be2, Be3, . . . ) at at least onedetermined frequency ω_(i) in response to the transmission signal thatis sent to it by the generator, at least one receiver comprising atleast one (Nr) receiver coil (R1, R2, R3, . . . ) and a measuringdevice, which is connected to the at least one receiver coil (R1, R2,R3, . . . ) and which supplies at least one measurement Ip_(i) of areceiving magnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13,Br23, Br33, . . . ) respectively induced by the transmitting magneticfield (Be1, Be2, Be3, . . . ) in each receiver coil (R1, R2, R3, . . .), in such a way as to supply several measurements Ip_(i) for i rangingfrom 1 to N, a processing unit (25) comprising a field model making itpossible to compute a position (P) and/or an orientation (Q) of thereceiver by computing a prediction H_(i) of the measurements as afunction of a criterion (C) computed as a function of an error E_(i),itself computed with respect to the measurements Ip_(i), characterizedin that the error E_(i) is computed by successive iterations frominitial prescribed values of the prediction H_(i) as being thedifference between the measurements Ip_(i) and a disrupted model Hp_(i)of the measurements, according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is the disruption made to the measurements Ip_(i) by themagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the computation being carried out insuch a way as to minimize the criterion (C), at each iteration theprediction H_(i) is initialized at the prescribed initial values, thenare computed the parameter β then the Δ_(i) and the disrupted modelHp_(i) as a function of H_(i) and Ip_(i) according to the equations:$\beta = \frac{A^{\prime \; T} \cdot B^{\prime}}{{A^{\prime}}^{2}}$Δ_(i=)((Ip_(i)) − (H_(i)))/((H_(i)) + (H_(i))β ω_(i))Hp_(i) = H_(i) ⋅ (1 + Δ_(i) ⋅ (j + β ⋅ ω_(i))) where A′ is a vector, thecoordinates of which are respectively formed by: ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))], B′ is a vector, the coordinates of which are respectivelyformed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 5. The compensating method as claimed in anyone of claims 1 to 4, characterized in that the field model making itpossible to compute a position (P) and/or an orientation (Q) of thereceiver by computing the prediction H_(i) of the measurements as afunction of the criterion (C) uses a Levenberg-Marquardt minimizationalgorithm.
 6. The compensating method as claimed in any one of thepreceding claims, characterized in that the determined frequencies ω_(i)are separate from one another.
 7. The compensating method as claimed inany one of the preceding claims, characterized in that the transmitter(10) comprises a plurality (Ne) of transmitter coils (E1, E2, E3)respectively transmitting a plurality of transmitting magnetic fields(Be1, Be2, Be3), the measuring device measuring for each receiver coil(R1, R2, R3) a plurality of receiving magnetic fields (Br11, Br21, Br31;Br12, Br22, Br32; Br13, Br23, Br33) respectively induced by theplurality of transmitting magnetic fields (Be1, Be2, Be3) in thereceiver coil (R1, R2, R3) and forming the measurements Ip_(i) for iranging from 1 N.
 8. The compensating method as claimed in any one ofthe preceding claims, characterized in that the locator (1) comprises atransmitter coil transmitting at K different frequencies ω_(jk) and Jreceiver coils, the measuring device supplying the measurements Ip_(jk)for the index j ranging from 1 to J and the index k ranging from 1 to K,the processing unit (25) computes$\rho_{j} = \frac{\sum\limits_{k = 1}^{K}{u_{jk} \cdot ( {{H_{jk}}^{2} + {{Ip}_{jk}}^{2} - {2 \cdot v_{jk}}} )}}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}$and$\beta = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jk} \cdot ( {v_{jk} - {H_{jk}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jk}^{2}}}$with v_(jk) = (H_(jk))⋅(Ip_(jk)) + (H_(jk))⋅(Ip_(jk))u_(jk) = ((H_(jk))⋅(Ip_(jk)) − (H_(jk))⋅(Ip_(jk))) ⋅ ω_(jk)Ip_(jk) = H_(jk) ⋅ (1 + Δ_(jk) ⋅ (j + β ⋅ ω_(jk)))$\Delta_{jk} = {\rho_{j}\frac{\omega_{jk}}{1 + ( {\beta \cdot \omega_{jk}} )^{2}}}$where H_(jk) is the prediction, ρ_(j) is the intensity of thedisruption, Hp_(jk) is the disrupted model and Hp_(jk)−Ip_(jk)=0.
 9. Thecompensating method as claimed in any one of the preceding claims,characterized in that the locator (1) comprises L transmitter coils or Ltransmitters (10), which transmit at K different frequencies ω_(jkl),and J receiver coils, the measuring device supplying the measurementsIp_(jkl) for the index j ranging from 1 to J, the index k ranging from lto K and the index l ranging from l to L, the processing unit (25)computes$\rho_{jl} = \frac{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {{H_{jkl}}^{2} + {{Ip}_{jkl}}^{2} - {2 \cdot v_{jkl}}} )}}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}$and$\beta_{l} = \frac{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{u_{jkl} \cdot ( {v_{jkl} - {H_{jkl}}^{2}} )}}}{\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}u_{jkl}^{2}}}$with v_(jkl) = (H_(jkl))⋅(Ip_(jkl)) + (H_(jkl))(Ip_(jkl))u_(jkl) = ((H_(jkl))⋅(Ip_(jkl)) − (H_(jkl))⋅(Ip_(jkl))) ⋅ ω_(jkl)Ip_(jkl) = H_(jkl) ⋅ (1 + Δ_(jkl) ⋅ (j + β ⋅ ω_(jkl)))$\Delta_{jkl} = {\rho_{j}\frac{\omega_{jkl}}{1 + ( {\beta \cdot \omega_{jkl}} )^{2}}}$where H_(jkl) is the prediction, ρ_(jl) is the intensity of thedisruption, Hp_(jkl) is the disrupted model and Hp_(jkl)−Ip_(jkl)=0. 10.A magnetic locator (1) comprising: at least one transmitter comprisingat least one (Ne) transmitter coil (E1, E2, E3) and at least onegenerator able to generate at least one transmission signal, connectedto the at least one transmitter coil (E1, E2, E3), so that the at leastone transmitter coil (E1, E2, E3) is able to transmit at least onetransmitting magnetic field (Be1, Be2, Be3) at at least one determinedfrequency ω_(i) in response to the transmission signal that is sent toit by the generator, at least one receiver comprising at least one (Nr)receiver coil (R1, R2, R3) and a measuring device, which is able to beconnected to the at least one receiver coil (R1, R2, R3) and which isable to supply at least one measurement Ip_(i) of a receiving magneticfield (Br11, Br21, Br31; Br12, Br22, Br32; Br13, Br23, Br33)respectively induced by the transmitting magnetic field (Be1, Be2, Be3)in each receiver coil (R1, R2, R3), to supply several measurementsIp_(i) for i ranging from 1 to N, a processing unit (25) comprising afield model making it possible to compute a position (P) and/or anorientation (Q) of the receiver by computing a prediction H_(i) of themeasurements as a function of a criterion (C) computed as a function ofan error E_(i), itself computed with respect to the measurements Ip_(i),characterized in that the processing unit (25) is configured so that theerror E_(i) is computed by successive iterations from initial prescribedvalues of the prediction H_(i) as being the difference between themeasurements Ip_(i) and a disrupted model Hp_(i) of the measurements,according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is a disruption made to the measurements Ip_(i) by amagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the processing unit (25) beingconfigured to carry out the computation in such a way as to minimize thecriterion (C), the processing unit (25) being configured to implementthe following steps at each iteration: the prediction H_(i) isinitialized at the prescribed initial values, then are computed Δ_(i),the parameter β so as to minimize the vector A·β−B over its coordinates,and the disrupted model Hp_(i) as a function of H_(i) and Ip_(i)according to the equations:Δ_(i)=[

(H _(i))·

(Ip _(i))−

(H _(i))·

(Ip _(i))]/[

(H _(i))²+

(H _(i))²],Hp _(i) =H _(i)·(1+Δ_(i)·(j+βω _(i))), where A is a vector, the firstand second coordinates of which are respectively formed by:A _(2i)=Δ_(i)·

(H _(i))·ω_(i) and A _(2i+1)=Δ_(i)·

(H _(i))·ω_(i), B is a vector, the first and second coordinates of whichare respectively formed by:B _(2i)=

(Ip _(i))−

(H _(i))+Δ_(i)·

(H _(i)) and B _(2i+1)=

(Ip _(i))−

(H _(i))−Δ_(i)·

(H _(i)), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 11. A magnetic locator (1) comprising: atleast one transmitter comprising at least one (Ne) transmitter coil (E1,E2, E3) and at least one generator able to generate at least onetransmission signal, connected to the at least one transmitter coil (E1,E2, E3), so that the at least one transmitter coil (E1, E2, E3) is ableto transmit at least one transmitting magnetic field (Be1, Be2, Be3) atat least one determined frequency (o in response to the transmissionsignal that is sent to it by the generator, at least one receivercomprising at least one (Nr) receiver coil (R1, R2, R3) and a measuringdevice, which is able to be connected to the at least one receiver coil(R1, R2, R3) and which is able to supply at least one measurement Ip_(i)of a receiving magnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13,Br23, Br33) respectively induced by the transmitting magnetic field(Be1, Be2, Be3) in each receiver coil (R1, R2, R3), to supply severalmeasurements Ip_(i) for i ranging from 1 to N, a processing unit (25)comprising a field model making it possible to compute a position (P)and/or an orientation (Q) of the receiver by computing a predictionH_(i) of the measurements as a function of a criterion (C) computed as afunction of an error E_(i), itself computed with respect to themeasurements Ip_(i), characterized in that the processing unit (25) isconfigured so that the error E_(i) is computed by successive iterationsfrom prescribed initial values of the prediction H_(i) as being thedifference between the measurements Ip_(i) and a disrupted model Hp_(i)of the measurements, according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is a disruption made to the measurements Ip_(i) by amagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the processing unit (25) beingconfigured to carry out the computation in such a way as to minimize thecriterion (C), the processing unit (25) being configured to implementthe following steps at each iteration: the prediction H_(i) isinitialized at the prescribed initial values, then are computed Δ_(i),the parameter β and the disrupted model Hp_(i) as a function of H_(i)and Ip_(i) according to the equations$\Delta_{i} = {\lbrack {{{( H_{i} ) \cdot}( {Ip}_{i} )} - {{( H_{i} ) \cdot}( {Ip}_{i} )}} \rbrack/\lbrack {( {{( H_{i} )^{2}} + {( H_{i} )^{2}}} \rbrack,{\beta = {{\frac{A^{T} \cdot B}{{A}^{2}}{Hp}_{i}} = {H_{i} \cdot ( {1 + {\Delta_{i} \cdot ( {j + {\beta \cdot \omega_{i}}} )}} )}}},} }$where Δ is a vector, the first and second coordinates of which arerespectively formed by: A_(2i)=Δ_(i)·

(H_(i))·ω_(i) and A_(2i+1)=Δ_(i)·

(H_(i))·ω_(i), B is a vector, the first and second coordinates of whichare respectively formed by: B_(2i)=

(Ip_(i))−

(H_(i))+Δ_(i)·

(H_(i)) and B_(2i+1)=

(Ip_(i))−

(H_(i))−Δ_(i)·

(H_(i)), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 12. A magnetic locator (1) comprising: atleast one transmitter comprising at least one (Ne) transmitter coil (E1,E2, E3) and at least one generator able to generate at least onetransmission signal, connected to the at least one transmitter coil (E1,E2, E3), so that the at least one transmitter coil (E1, E2, E3) is ableto transmit at least one transmitting magnetic field (Be1, Be2, Be3) atat least one determined frequency ω_(i) in response to the transmissionsignal that is sent to it by the generator, at least one receivercomprising at least one (Nr) receiver coil (R1, R2, R3) and a measuringdevice, which is able to be connected to the at least one receiver coil(R1, R2, R3) and which is able to supply at least one measurement Ip_(i)of a receiving magnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13,Br23, Br33) respectively induced by the transmitting magnetic field(Be1, Be2, Be3) in each receiver coil (R1, R2, R3), to supply severalmeasurements Ip_(i) for i ranging from 1 to N, a processing unit (25)comprising a field model making it possible to compute a position (P)and/or an orientation (Q) of the receiver by computing a predictionH_(i) of the measurements as a function of a criterion (C) computed as afunction of an error E_(i), itself computed with respect to themeasurements Ip_(i), characterized in that the processing unit (25) isconfigured so that the error E_(i) is computed by successive iterationsfrom prescribed initial values of the prediction H_(i) as being thedifference between the measurements Ip_(i) and a disrupted model Hp_(i)of the measurements, according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is a disruption made to the measurements Ip_(i) by amagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the processing unit (25) beingconfigured to carry out the computation in such a way as to minimize thecriterion (C), the processing unit (25) being configured to implementthe following steps at each iteration: the prediction H_(i) isinitialized at the prescribed initial values, then are computed theparameter β so as to minimize the vector A′·D+B′ over its coordinates,then the Δ_(i) and the disrupted model Hp_(i) as a function of H_(i) andIp_(i) according to the equations:Δ_(i)=(

(Ip _(i))−

(H _(i)))/(

(H _(i))+

(H _(i))βω_(i))Hp _(i) =H _(i)·(1+Δ_(i)·(j+·ω _(i))) where A′ is a vector, thecoordinates of which are respectively formed by: ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))], B′ is a vector, the coordinates of which are respectivelyformed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 13. A magnetic locator (1) comprising: atleast one transmitter comprising at least one (Ne) transmitter coil (E1,E2, E3) and at least one generator able to generate at least onetransmission signal, connected to the at least one transmitter coil (E1,E2, E3), so that the at least one transmitter coil (E1, E2, E3) is ableto transmit at least one transmitting magnetic field (Be1, Be2, Be3) atat least one determined frequency ω_(i) in response to the transmissionsignal that is sent to it by the generator, at least one receivercomprising at least one (Nr) receiver coil (R1, R2, R3) and a measuringdevice, which is able to be connected to the at least one receiver coil(R1, R2, R3) and which is able to supply at least one measurement Ip_(i)of a receiving magnetic field (Br11, Br21, Br31; Br12, Br22, Br32; Br13,Br23, Br33) respectively induced by the transmitting magnetic field(Be1, Be2, Be3) in each receiver coil (R1, R2, R3), to supply severalmeasurements Ip_(i) for i ranging from 1 to N, a processing unit (25)comprising a field model making it possible to compute a position (P)and/or an orientation (Q) of the receiver by computing a predictionH_(i) of the measurements as a function of a criterion (C) computed as afunction of an error E_(i), itself computed with respect to themeasurements Ip_(i), characterized in that the processing unit (25) isconfigured so that the error E_(i) is computed by successive iterationsfrom prescribed initial values of the prediction H_(i) as being thedifference between the measurements Ip_(i) and a disrupted model Hp_(i)of the measurements, according to the equationE _(i) =Ip _(i) −Hp _(i), the disrupted model Hp_(i) of the measurementsverifying the following equations${{Hp}_{\;^{i}} = {H_{i} + P_{i}}},{P_{i} = {\rho_{i}\frac{{jH}_{i}}{H_{i}}e^{j\; \alpha_{i}}}},{\alpha_{i} = {- {\arctan ( {\beta \cdot \omega_{i}} )}}},$where P_(i) is a disruption made to the measurements Ip_(i) by amagnetic-field-disrupting material (3), ρ_(i) is the intensity of thedisruption, α_(i) is a phase shift angle caused by themagnetic-field-disrupting material (3), β being a parameter of themagnetic-field-disrupting material (3), the parameter β being identicalfor all the measurements Ip_(i), the processing unit (25) beingconfigured to carry out the computation in such a way as to minimize thecriterion (C), the processing unit (25) being configured to implementthe following steps at each iteration: the prediction H_(i) isinitialized at the prescribed initial values, then are computed theparameter β then the Δ_(i) and the disrupted model Hp_(i) as a functionof H_(i) and Ip_(i) according to the equations:$\beta = \frac{A^{\prime \; T} \cdot B^{\prime}}{{A^{\prime}}^{2}}$Δ_(i=)((Ip_(i)) − (H_(i)))/((H_(i)) + (H_(i))β ω_(i))Hp_(i) = H_(i) ⋅ (1 + Δ_(i) ⋅ (j + β ⋅ ω_(i))) where A′ is a vector, thecoordinates of which are respectively formed by: ω_(i)·[

(H_(i))·

(Ip_(i))−

(Ip_(i))·

(H_(i))], B′ is a vector, the coordinates of which are respectivelyformed by:

(H_(i))²+

(H_(i))²−(

(H_(i))·

(Ip_(i))+

(H_(i))·(Ip_(i))), for i ranging from 1 to N, where

(H_(i)) is the real part of the prediction H_(i),

(H_(i)) is the imaginary part of the prediction H_(i),

(Ip_(i)) is the real part of the measurement Ip_(i),

(Ip_(i)) is the imaginary part of the measurement Ip_(i), then the errorE_(i) is computed, then the criterion C is computed according to theequation ${C = {\sum\limits_{i = 0}^{N}{E_{i}}^{2}}},$ then theprediction H_(i) corresponding to the criterion C is computed by thefield model, this computed prediction H_(i) being used for the followingiteration until the computed criterion C becomes less than a prescribednon-zero positive bound η.
 14. The magnetic locator (1) as claimed inany one of claims 10 to 13, characterized in that the field model makingit possible to compute a position (P) and/or an orientation (Q) of thereceiver by computing the prediction H_(i) of the measurements as afunction of the criterion (C) uses a Levenberg-Marquardt minimizationalgorithm.
 15. A computer program, comprising code instructions forimplementing the method for compensating a magnetic locator in thepresence of at least one magnetic-field-disrupting material as claimedin any one of claims 1 to 9, when the computer program is executed on acalculator.